The formation of halo currents in a peripheral tokamak plasma is simulated numerically with 1.5-dimensional resistive code DINA. Results from numerical calculations of the vertical displacement episode for a tokamak on the scale of the ITER reactor are presented. In the peripheral plasma region, the poloidal and toroidal components of the halo current are estimated for an electron temperature on the order of 50 eV in the case of an uncontrolled upward motion of the plasma column. Numerical calculations incorporating halo currents show that the vertical velocity of the plasma column decreases during the vertical displacement episode.